Abstract: A method for the continuous production of crystalline ethylene-propylene block copolymers containing propylene as the major component and having excellent physical properties as that by a batch process in a slurry-phase by homopolymerizing propylene and then copolymerizing ethylene and propylene in the presence of an inert hydrocarbon solvent and a stereoregular polymerization catalyst in polymerization vessels connected in series, which is characterized by homopolymerizing propylene in three polymerization vessels, wherein the inner pressure of the vessels is decreased in order so as to make the inner-pressure difference between each consecutive two vessels from 1 to 3 kg/cm.sup.